Showing papers in "Bulletin of Mathematical Biology in 2003"

TL;DR: A model for electrical activity of cardiac membrane which incorporates only an inward and an outward current is introduced, which naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval.

TL;DR: A model for chemotaxis in response to a combination of chemoattractant and chemorepellent signaling chemicals is developed and predicted that periodic patterns in cell and chemical distributions can evolve under local attraction, long-ranged repulsion, and other constraints on concentrations and diffusion coefficients of the chemotactic signals.

TL;DR: The total quasi-steady state approximation (tQSSA) for the irreversible Michaelis-Menten scheme is derived in a consistent manner and it is found that self-consistency of the initial transient guarantees the uniform validity of the tSSA.

TL;DR: The results reveal that optimal antiangiogenic monotherapy gives a large initial injection to attain a 20:1 ratio of tumor cell volume to supporting vasculature volume, and thereafter maintains this 20: 1 ratio via a continuous dose rate that is intensified over time.

TL;DR: A new model framework for studying vascular tumour growth is presented, in which the blood vessel density is explicitly considered, and is able to reproduce tumour structure that is found in vivo in certain cases.

TL;DR: Results show that when mobility rates are very low, as in this region, quarantine practices must be highly effective before they alter disease patterns significantly, and that a policy of introducing quarantine at the earliest possible time may not always lead to the greatest reduction in cases of a disease.

TL;DR: Traveling waves are analyzed in a model of the hantavirus infection in deer mice, predicting the existence of two kinds of wave phenomena and the dependence of the delay on system parameters.

TL;DR: A mathematical model for colony expansion that is derived through consideration of the growth characteristics on the microscale and provides important predictions on the functional consequences of the redistribution of internally-located material is presented.

TL;DR: This paper introduces a mathematical function, called image function, which allows the calculation of the value of the logical parameter associated with a logical variable depending on the state of the system, and shows how all steady states can be derived as solutions to a system of steady-state equations.

TL;DR: It is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.

TL;DR: An analytical formula is derived which appears to be in a very good agreement with the value of the correlation length of the system parameters and may lead to a new understanding of some well-known experimental and field data and affect the choice of an adequate model of chaotic dynamics in biological and chemical systems.

TL;DR: A one-dimensional model of a growing Pseudomonas aeruginosa biofilm is examined and the prediction of a critical pH threshold, above which quorum sensing is not possible at any depth, is predicted.

TL;DR: A nonlinear system of delay differential equations to model the concentrations of five hormones important for regulation and maintenance of the menstrual cycle predicts serum levels of ovarian and pituitary hormones which agree with data in the literature for normally cycling women and indicates the existence and stability of an abnormal cycle.

TL;DR: These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.

TL;DR: An evolutionary link between allocation strategies and expected life span is suggested and it is suggested that when the mortality risk of organisms with small size is much higher than those of large size, indeterminate growers can be superior.

TL;DR: In this paper, the evolution of a tumour cord after treatment is investigated by extensive numerical simulations on the basis of a mathematical model developed by Bertuzzi et al. The model is formulated in cylindrical symmetry adopting the continuum approach, and takes into account the influence of oxygen level on the proliferation and death rate of cells, the volume reduction due to disgregation of dead cells, and the cell killing effects of radiation and drugs.

TL;DR: A multi-patch multi-species model in which the percapita emigration rate of one species depends on the density of some other species focuses on Turing instability to examine if and when this cross-emigration response has crucial effects.

TL;DR: It is shown that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment and a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity is suggested.

TL;DR: The results not only confirm that selection is the result of a trail modulation according to food quality but also show the existence of an optimal quantity of laid pheromone for which the selection of a source is at the maximum, whatever the difference between the two sources might be.

TL;DR: When the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are known to be linear it is possible to calculate their survival parameters from curves obtained under nonisothermal conditions, provided that the temperature history satisfies certain simple mathematical requirements.

TL;DR: This work applied Markov chain theory in an attempt to describe the interaction between the antibiotic paromomycin and the packaging region of the RNA in Type-1 HIV and developed a stochastic matrix that codifies the probabilities of interaction between specific nucleotides of HIV-RNA and the antibiotic.

TL;DR: A new model framework for the urine concentrating mechanism in the outer medulla of the rat kidney is formulated and it is shown that the method generates approximations that are second-order accurate in space and that exhibit mass conservation.

TL;DR: The ability of a cell to sense gradients persists even when the cell is immobilized, suggesting that important features of gradient sensing can be studied in isolation, decoupling this phenomenon from the movement of the cell.

TL;DR: Bifurcation analysis shows that both models give possible mechanisms for dichotomous branching of the growing tips, both of which are two-morphogen reaction-diffusion systems on the surface of a hemispherical shell.

TL;DR: It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured, under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

TL;DR: The immune system is used as a prototype for representing individually the elementary interactions between their microscopic components, and a mixture of microscopic simulation systems describing each reaction separately, and continuous methods describing the average behaviour of the agents are proposed.

TL;DR: A general mathematical framework is presented for studying problems of this type, which may be adapted to many host-parasite systems, and used to examine the optimal virus production scheduling problem from the perspective of the virus.

TL;DR: Analysis of the occurrence of viral blips in 123 treated HIV-infected patients shows that patients do not share a common probability distribution of blip amplitude and thus reject the hypothesis that blips are solely due to assay variation.

TL;DR: A stochastic Hindmarsh-Rose model is studied using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern, which exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude.